%% plain tex file

\def\pgfsysdriver{pgfsys-pdftex.def}
\input pgfplots.tex
\pgfplotsset{compat=1.3}% <-- moves axis labels near ticklabels (respects tick label widths)

Using plain-\TeX.

\tikzpicture
	\loglogaxis
	\addplot coordinates {
		(1,1)
		(16,16)
		(32,64)
	};
	\endloglogaxis
\endtikzpicture

\tikzpicture
	\loglogaxis[
		xlabel=Cost,
		ylabel=Error]
	\addplot coordinates {
		(5,     8.31160034e-02)
		(17,    2.54685628e-02)
		(49,    7.40715288e-03)
		(129,   2.10192154e-03)
		(321,   5.87352989e-04)
		(769,   1.62269942e-04)
		(1793, 4.44248889e-05)
		(4097, 1.20714122e-05)
		(9217, 3.26101452e-06)
	};
	\addplot coordinates {
		(7,     8.47178381e-02)
		(31,    3.04409349e-02)
		(111,   1.02214539e-02)
		(351,   3.30346265e-03)
		(1023,  1.03886535e-03)
		(2815,  3.19646457e-04)
		(7423,  9.65789766e-05)
		(18943, 2.87339125e-05)
		(47103, 8.43749881e-06)
	};
	\legend{Case 1,Case 2}
	\endloglogaxis
\endtikzpicture

\bye
